Cornet is the No. 3 seed this week but the highest left the tournament, which has a formal title of Grand Prix Sar La Princesse Lalla Meryem. Top-seeded Dominika Cibulkova withdrew from the event and No. 2-seeded Sorana Cirstea lost a first-round match Monday.
Cornet, however, advanced by beating Fatima Zahrae El Allami 6-1, 6-1 in an hour. One of the games Cornet lost was a service break but she still took 71 percent of the points on serve and two-thirds when receiving serve.
Fourth-seeded Kaia Kanepi got past Anabel Medina Garrigues 4-6, 6-3, 6-2. She ended up with six breaks, including three in the third set.
Kiki Bertens, the fifth seed and defending champion, defeated Timea Babos 7-5, 6-2, while No. 7-seeded Kristina Mladenovic took out Alexandra Cadantu 6-4, 4-6, 6-4 in a 2 1/2-hour battle, and ninth-seeded Tsvetana Pironkova stopped Karolina Pliskova 7-5, 6-1.
In other first-round matches Tuesday Lourdes Dominguez Lino beat Misaki Doi 6-2, 4-6; 6-2; Mandy Minella advanced over Estrella Cabeza Candela 7-6 (7-3), 4-6, 7-5; Silvia Soler-Espinosa defeated Michaela Honcova 7-6 (7-4), 6-2; Simona Halep eliminated Nina Bratchikova 6-1, 6-3; and Karin Knapp rolled over Lina Qostal 6-0, 6-1.